​ If y = x + √(x^2 - 1), show that (x^2 – 1)y2 + xy1 – y = 0 ​

Question

If y = x + \(\sqrt{x^2 - 1}\), show that (x² – 1)y₂ + xy₁ – y = 0

Answer 1

 y = x + \(\sqrt{x^2 - 1}\), differentiate w.r.t x

∴ (x² – 1) y₁² = y² 

Differentiate agin w.r.t x 

(x² – 1)2y₁y₂ + y₁²(2x) = 2y .y₁ (÷ 2y₁ we get) 

(x² – 1)y₂ + xy₁ – y = 0 

Hence proved